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Computing floating-point gröbner bases stably
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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2007 international workshop on Symbolic-numeric computation table of contents
London, Ontario, Canada
SESSION: Contributed full papers table of contents
Pages: 180 - 189  
Year of Publication: 2007
ISBN:978-1-59593-744-5
Authors
Tateaki Sasaki  University of Tsukuba, Tsukuba-Shi, Japan
Fujio Kako  Nara Women's University, Nara-shi, Japan
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
ACM: Association for Computing Machinery
Publisher
ACM  New York, NY, USA
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ABSTRACT

Computing floating-point gröbner bases stably.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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J.-C. Faugère.A new e cient algorithm for computing Gröbner bases (F 4 .J. Pure Appl. Algebra 139 (1999), 61--88.
 
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E. Fortuna, P. Gianni and B. Trager. Degree reduction under specialization. J. Pure Appl. Algebra 164 (2001),153--164.
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F. Kako and T. Sasaki. Proposal of "effective" floating-point number. Preprint of Univ.Tsukuba, May 1997 (unpublished).
 
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A. Kondratyev, H. J. Stetter and S. Winkler. Numerical computation of Gr öbner bases. Proceedings of CASC2004 (Computer Algebra in Scientific Computing) 295--306, St. Petersburg, Russia, 2004.
 
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B. Mourrain. Pythagore's dilemma, symbolic-numeric computation, and the border basis method. Symbolic-Numeric Computations (Trends in Mathematics)223--243, Birkhä user Verlag, 2007.
 
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T. Ohyoshi. Effectiveness of "efloat numbers "in approximate algebra (in Japanese). Master thesis of Univ. Tsukuba,March 2003.
 
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T. Sasaki, T. Kitamoto and F. Kako.Error analysis of power-series roots of multivariate algebraic equation. March 1994 (submitted).
 
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M. Sanuki and T. Sasaki. Computing approximate GCD's in ill-conditioned cases. This proceedings.
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H. J. Stetter. Approximate Gröbner bases -- an impossible concept? Proceedings of SNC2005 (Symbolic-Numeric Computation)235--236, Xi'an, China,2005.
 
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H. J. Stetter. Proposal of the algorithmic use of the BKK-number in the algebraic reduction of a 0-dimensional polynomial system.Symbolic-Numeric Computations (Trends in Mathematics)245--267, Birkhäuser Verlag, 2007.
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C. Traverso. Syzygies, and the stabilization of numerical Buchberger algorithm. Proceedings of LMCS2002 (Logic, Mathematics and Computer Science) 244--255, RISC-Linz, Austria, 2002.
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V. Weispfenning. Gröbner bases for inexact input data. Proceedings of CASC2003 (Computer Algebra in Scientific Computing) 403--411, Passau, Germany, 2002.

Collaborative Colleagues:
Tateaki Sasaki: colleagues
Fujio Kako: colleagues